Related papers: The Floyd-Warshall Algorithm, the AP and the TSP I…
We present algorithmic improvements to the overlap Hybrid Monte Carlo algorithm, including preconditioning techniques and improvements to the correction step, used when one of the eigenvalues of the Kernel operator changes sign, which is…
We compute the two-mass contributions to the polarized massive operator matrix element $A_{gg,Q}^{(3)}$ at third order in the strong coupling constant $\alpha_s$ in Quantum Chromodynamics analytically. These corrections are important…
We study the metric $s$-$t$ path Traveling Salesman Problem (TSP). [An, Kleinberg, and Shmoys, STOC 2012] improved on the long standing $\frac{5}{3}$-approximation factor and presented an algorithm that achieves an approximation factor of…
This paper proposes an accelerated version of Feasible Sequential Linear Programming (FSLP): the AA($d$)-FSLP algorithm. FSLP preserves feasibility in all intermediate iterates by means of an iterative update strategy which is based on…
Quantum phase transitions between the magnetically ordered and disordered states are studied for the two-dimensional antiferromagnetic quantum spin systems with ladder, plaquette, and mixed-spin structures. Starting with properly chosen…
We discuss the problem of factorisation of the symmetric Macdonald polynomials and present the obtained results for the cases of 2 and 3 variables.
Most decision and optimization problems encountered in practice fall into one of two categories with respect to any particular solving method or algorithm: either the problem is solved quickly (easy) or else demands an impractically long…
We describe an explicit algorithm to factorize an even antisymmetric N^2 matrix into triangular and trivial factors. This allows for a straight forward computation of Pfaffians (including their signs) at the cost of N^3/3 flops.
In this paper we provide an introduction to the Frank-Wolfe algorithm, a method for smooth convex optimization in the presence of (relatively) complicated constraints. We will present the algorithm, introduce key concepts, and establish…
Feasibility pump (FP) is a successful primal heuristic for mixed-integer linear programs (MILP). The algorithm consists of three main components: rounding fractional solution to a mixed-integer one, projection of infeasible solutions to the…
This chapter describes modal decompositions in the framework of matrix factorizations. We highlight the differences between classic space-time decompositions and 2D discrete transforms and discuss the general architecture underpinning…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
We compute the next-to-next-to-leading order (NNLO) QCD corrections to the first five moments of six event shape variables related to three-particle final states in electron-positron annihilation; the thrust, the heavy jet mass, the…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized P\'olya-Aeppli process. It is shown that these processes…
It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time \tau using periodic-orbit theory. Two types of contributing pairs of orbits were…
The three-loop QCD corrections to the $\rho$ parameter from top and bottom quark loops are calculated. The result differs from the one recently calculated by Avdeev et al. As function of the pole mass the numerical value is given by…
We provide a polynomial time 4/3 approximation algorithm for TSP on metrics arising from the metric completion of cubic 3-edge connected graphs.
This dissertation addresses a topic that I have worked on over the past decade: the automation of next-to-leading order electroweak corrections in the Standard Model of particle physics. After introducing the basic concepts and techniques…
We introduce a new class of Frank-Wolfe algorithms for minimizing differentiable functionals over probability measures. This framework can be shown to encompass a diverse range of tasks in areas such as artificial intelligence,…